1. The problem asks: How much of the circle is shaded? Write your answer as a fraction in simplest form. 2. We are given two fractions: $\frac{1}{2}$ and $\frac{4}{9}$. These likely represent parts of the circle. 3. To find the total shaded fraction, we add these two fractions: $$\frac{1}{2} + \frac{4}{9}$$ 4. Find a common denominator for $2$ and $9$, which is $18$. 5. Convert each fraction: $$\frac{1}{2} = \frac{9}{18}$$ $$\frac{4}{9} = \frac{8}{18}$$ 6. Add the fractions: $$\frac{9}{18} + \frac{8}{18} = \frac{9+8}{18} = \frac{17}{18}$$ 7. The fraction $\frac{17}{18}$ is already in simplest form because $17$ is a prime number and does not share any factors with $18$. 8. Therefore, the shaded part of the circle is $\frac{17}{18}$. Final answer: $\boxed{\frac{17}{18}}$